Theorem botel 33906

Description: An inference for bottom elimination. (Contributed by Giovanni Mascellani, 24-May-2019.)

Hypothesis

Ref	Expression
botel.1	|- ( ph -> F. )

Assertion

Ref	Expression
botel	|- ( ph -> ps )

Proof of Theorem botel

Step	Hyp	Ref	Expression
1		botel.1	. 2 |- ( ph -> F. )
2		falim 1498	. 2 |- ( F. -> ps )
3	1, 2	syl 17	1 |- ( ph -> ps )

Syntax hints:   -> wi 4   F. wfal 1488

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 197  df-tru 1486  df-fal 1489

This theorem is referenced by: (None)